Course details

# Theoretical Computer Science

TIN Acad. year 2006/2007 Winter semester 5 credits

Guarantor

Language of instruction

Completion

Time span

Assessment points

Department

Lecturer

Instructor

Hrubý Martin, Ing., Ph.D. (DITS FIT BUT)

Marek Vladimír, Ing. (DITS FIT BUT)

Vojnar Tomáš, prof. Ing., Ph.D. (DITS FIT BUT)

Subject specific learning outcomes and competences

Generic learning outcomes and competences

Learning objectives

Prerequisite kwnowledge and skills

Study literature

- Kozen, D.C.: Automata and Computability, Springer-Verlag, New Yourk, Inc, 1997. ISBN 0-387-94907-0
- Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation, Addison Wesley, 2nd ed., 2000. ISBN 0-201-44124-1

Fundamental literature

- Kozen, D.C.: Automata and Computability, Springer-Verlag, New Yourk, Inc, 1997. ISBN 0-387-94907-0
- Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation, Addison Wesley, 2nd ed., 2000. ISBN 0-201-44124-1
- Martin, J.C.: Introduction to Languages and the Theory of Computation, McGraw-Hill, Inc., 3rd ed., 2002. ISBN 0-072-32200-4
- Brookshear, J.G. : Theory of Computation: Formal Languages, Automata, and Complexity, The Benjamin/Cummings Publishing Company, Inc, Redwood City, California, 1989. ISBN 0-805-30143-7
- Aho, A.V., Ullmann, J.D.: The Theory of Parsing,Translation and Compiling, Prentice-Hall, 1972. ISBN 0-139-14564-8

Syllabus of lectures

- An overview of the applications of the formal language theory, the modelling and decision power of formalisms, operations over languages.
- Regular languages and their properties, Kleene's theorem, Nerod's theorem, Pumping lemma.
- Minimalization of finite-state automata, the relation of indistinguishability of automata states, construction of a reduced finite-state automaton.
- Closure properties of regular languages, regular languages as a Boolean algebra, decidable problems of regular languages.
- Context-free languages and their properties, normal forms of context-free grammars, unambiguous and deterministic context-free languages, Pumping lemma for context-free languages.
- Closure properties of context-free languages, closedness wrt. substitution and its consequences, decidable problems of context-free languages.
- Turing machines (TMs), the language accepted by a TM, recursively enumerable and recursive languages and problems, TMs and functions, methods of constructing TMs.
- Modifications of TMs, TMs with a tape infinite on both sides, with more tapes, nondeterministic TMs, automata with two push-down stacks, automata with counters.
- TMs and type-0 languages, diagonalisation, properties of recursively enumerable and recursive languages, linearly bounded automata and type-1 languages.
- Computable functions, initial functions, primitive recursive functions, mu-recursive functions, the relation of TMs and computable functions.
- The Church-Turing thesis, universal TMs, undecidability, the halting problem, reductions, the Post's correspondence problem.
- Undecidable problems of the formal language theory.
- An introduction to the computational complexity, Turing complexity, the P and NP classes and beyond.

Syllabus - others, projects and individual work of students

- A homework on regular languages and finite-state automata.
- A homework on context-free languages.
- A homework on Turing machines.
- A homework on computable functions.

Progress assessment

Controlled instruction

Exam prerequisites